LEARN NC

CareerStart lessons: Grade eight

2.9 Careers in banking: Working with exponential growth

By Debbie Brooks, Peggy Dickey, and Jan Sullivan

Provided by CareerStart

Essential question: How is the concept of exponential growth important in banking careers?

Learning outcomes

Students will solve problems involving exponential growth.

Teacher planning

Materials needed

  • Worksheet: “Money in the Bank” (Includes answer key)
  • Overhead projector (or other projection device) and pens
  • Overhead transparency: Graph paper
  • Graphing calculator

Time required for lesson

Approximately 55 minutes

Activities

  1. Review the career information about bankers before beginning the lesson. (See Career Information below.
  2. (5 minutes) Review with students the equation for exponential growth: y=a(b)x or y = a(1+rate)x, where a represents the initial amount, b the rate (percent) in which the initial amount is increasing by and x represents time (in years).
    • How does this equation differ from a linear equation?
      (Rate is not constant, but increases at a certain percent each year)
  3. (10 minutes) Have students read over the problem on the worksheet. Ask a volunteer to give the equation for Javier’s investment (y = 1500(1.04)x).
    • What value represents Javier’s initial investment? ($1500)
    • What value replaces b? Why? (1.04 because his investments are increasing 4% each year. 4% of his balance is added to the previous year’s balance.)
    • Enter the equation into the y= of the graphing calculator.
    • Complete the table in Question 2 and plot the given ordered pairs.
  4. (10 minutes) Ask a volunteer to give the equation for Charlie’s investment
    (y = 500(1.12)x)
    • What value represents Charlie’s initial investment? ($500)
    • What value replaces b? Why? (1.12 because his investments are increasing 12% each year. 12% of his balance is added to the previous year’s balance)
    • Enter the equation into the y= of the graphing calculator.
    • Complete the table in Question 2 and plot the given ordered pairs.
  5. (10 minutes) Answer Question 3a - e looking at the table and graph. Students may also use the table function on their graphing calculators in order to continue their table.
  6. (5 minutes) Discuss question 4 with the students. Challenge the students with a case in which the investment would lose 4% or 12%: What would happen to the value of b?
  7. (5 minutes) Discuss question 5 with the students. How do they see the value of a change in the table? Graph?
  8. (10 minutes) Conclude the lesson by brainstorming other careers that may use exponential notation. (i.e. banking, investments, stocks, census workers (changes in population), biologist (rate of bacteria growth), real estate (appreciates), auto sales (depreciates). See Career Information below.

Career information

Some of the information below comes from the Bureau of Labor Statistics’ Occupational Outlook Handbook.

Bankers
Banks have traditionally offered savings and checking accounts and loans for homes and other purchases. Savings accounts are safe places to put money for future use with a small interest payment made to the depositor. These accounts are insured for up to $250,000 by the FDIC even if a bank fails. The money in your savings account is used by the bank to make loans to others. The interest is payment for the use of your money. Today, banks have increased their services to include other types of investments and insurance policies. These investments are offered with higher returns than savings accounts, but with risks. Money invested in stocks and bonds through the bank may increase or decrease in value. Bankers receive a commission on the money they invest for their clients and there are no guarantees to the investor that the investments will increase in value.

  • Education: bachelor’s degree
  • Pay: $27,000 - $52,000
  • Growth: Lower than average; 4% increase over the next 10 years
Automobile salesperson
Automobile salespeople sell cars, small trucks, and vans that are new or used. Salespeople work long hours including weekends to be available to the customer. The job can be stressful as each salesperson has a sales quota and earnings goal to meet. Due to these expectations, there is a lot of turnover in this position. Used cars depreciate in value and prices must be set based on the depreciation and condition of the car.

  • Education: high-school diploma
  • Pay: $30,000 - $40,000
  • Growth: average growth; 11% increase over the next 10 years

North Carolina curriculum alignment

Mathematics (2004)

Grade 9–12 — Algebra 1

  • Goal 4: Algebra - The learner will use relations and functions to solve problems.
    • Objective 4.04: Graph and evaluate exponential functions to solve problems.